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This study presents a thorough comparative analysis between post-Newtonian (PN) and numerically relativistic (NR) waveforms in eccentric orbits, covering nonspinning and spin-aligned configurations. The comparison examines frequency, amplitude, and phase characteristics of various harmonic modes, such as 22, 21, 33, 32, 44, 43, and 55 modes. The study utilizes eccentric PN waveforms based on 3PN quasi-Keplerian parameterization with 3PN radiative reaction, surpassing Newtonian quadrupole moment with higher-order moments. NR waveforms from RIT and SXS catalogs span mass ratios from 1/4 to 1, eccentricities up to 0.45, and durations exceeding $17000M$ across nonspinning and spin-aligned configurations. Focusing on the 22 mode, frequency comparisons between quadrupole and higher-order moments of $\Psi_4^{22}$ and $h^{22}$ were conducted. Amplitude comparisons revealed superior accuracy in quadrupole moments of $\Psi_4^{22}$. Analysis of total 180 sets of eccentric waveforms showed increasing fitting residuals with rising eccentricity, correlating with smaller mass ratios. Comparisons of initial eccentricity from PN fitting, 3PN quasi-Keplerian parameterization, and RIT/SXS catalogs revealed alignment discrepancies. Frequency, phase, and amplitude comparisons of 22 modes showed consistent inspiral behavior between PN and NR, with divergences near merger for nonspinning PN and pre-200M for spin-aligned PN., Comment: Comments are very welcome and it have been submitted to PRD with 18 figures

We have developed a method for constructing spectral approximations for convolution operators of Fredholm type. The algorithm we propose is numerically stable and takes advantage of the recurrence relations satisfied by the entries of such a matrix approximation. When used for computing the Fredholm convolution of two given functions, such approximations produce the convolution more rapidly than the state-of-the-art methods. The proposed approximation also leads to a spectral method for solving the Fredholm convolution integral equations and enables the computation of eigenvalues and pseudospectra of Fredholm convolution operators, which is otherwise intractable with existing techniques.

We propose a continuous approach for computing the pseudospectra of linear operators following a 'solve-then-discretize' strategy. Instead of taking a finite section approach or using a finite-dimensional matrix to approximate the operator of interest, the new method employs an operator analogue of the Lanczos process to work directly with operators and functions. The method is shown to be free of spectral pollution and spectral invisibility, fully adaptive, nearly optimal in accuracy, and well-conditioned. The advantages of the method are demonstrated by extensive numerical examples and comparison with the traditional method., Comment: 22 pages, 6 figures

Variational Quantum Eigensolver (VQE) provides a powerful solution for approximating molecular ground state energies by combining quantum circuits and classical computers. However, estimating probabilistic outcomes on quantum hardware requires repeated measurements (shots), incurring significant costs as accuracy increases. Optimizing shot allocation is thus critical for improving the efficiency of VQE. Current strategies rely heavily on hand-crafted heuristics requiring extensive expert knowledge. This paper proposes a reinforcement learning (RL) based approach that automatically learns shot assignment policies to minimize total measurement shots while achieving convergence to the minimum of the energy expectation in VQE. The RL agent assigns measurement shots across VQE optimization iterations based on the progress of the optimization. This approach reduces VQE's dependence on static heuristics and human expertise. When the RL-enabled VQE is applied to a small molecule, a shot reduction policy is learned. The policy demonstrates transferability across systems and compatibility with other wavefunction ansatzes. In addition to these specific findings, this work highlights the potential of RL for automatically discovering efficient and scalable quantum optimization strategies., Comment: 15 pages, 4 figures

Space-based gravitational wave (GW) detectors are expected to detect the stellar-mass binary black holes (SBBHs) inspiralling in the low-frequency band, which exist in several years before the merger. Accurate GW waveforms in the inspiral phase are crucial for the detection and analysis of those SBBHs. In our study, based on post-Newtonian (PN) models, we investigate the differences in the detection, accuracy requirement, and parameter estimation of SBBHs in the cases of LISA, Taiji, and their joint detection. We find that low-order PN models are sufficient for simulating low-mass ($\le 50\ \mathrm{M}_\odot$) SBBHs population. Moreover, for detectable SBBHs in space-based GW detectors, over 90% of the GW signals from low-order PN models meet accuracy requirement. Additionally, different PN models do not exhibit significant differences in Bayesian inference. Our research provides a comprehensive reference for balancing computational resources and the desired accuracy of GW waveform generation. It highlights the suitability of low-order PN models for simulating SBBHs and emphasizes their potential in the detection and parameter estimation of SBBHs., Comment: 16 pages, 11 figures

Many articles have partially studied the configuration of eccentric orbital binary black hole (BBH) mergers. However, there is a scarcity of systematic and comprehensive research on the effect of eccentricity on BBH dynamics. Thanks to the rich and numerous numerical relativistic simulations of eccentric orbital BBH mergers from RIT catalog, this paper aims to investigate the impact of initial eccentricity $e_0$ on various dynamic quantities such as merger time $T_{\text{merger}}$, peak luminosity $L_{\text{peak}}$ of gravitational waves, recoil velocity $V_f$, mass $M_f$, and spin $\alpha_f$ of merger remnants. We cover configurations of no spin, spin alignment, and spin precession, as well as a broad parameter space of mass ratio ranging from 1/32 to 1 and initial eccentricity from 0 to 1. For non-spinning BBH with an initial coordinate separation of $11.3M$ ($M$ is the total mass of BBH), we make the first discovery of a ubiquitous oscillation in the relationship between dynamic quantities $L_{\text{peak}}$, $V_f$, $M_f$, $\alpha_f$, and initial eccentricity $e_0$. Additionally, at $24.6M$, we observe the same oscillation phenomenon in the case of mass ratio $q=1$, but do not see it in other mass ratios, suggesting that this oscillation will be evident in numerical simulations with sufficiently dense initial eccentricity. abbreviated, Comment: 25 pages, 7 figures

Waveform models are important to gravitational wave data analysis. People recently pay much attention to the waveform model construction for eccentric binary black hole coalescence. Several Effective-One-Body Numerical-Relativity waveform models of eccentric binary black hole coalescence have been constructed. But none of them can treat orbit eccentricity and spin-precessing simultaneously. The current paper focuses on this problem. The authors previously have constructed waveform model for spin-aligned eccentric binary black hole coalescence $\texttt{SEOBNRE}$. Here we extend such waveform model to describe eccentric spin-precessing binary black hole coalescence. We calculate the 2PN orbital radiation-reaction forces and the instantaneous part of the decomposed waveform for a general spinning precessing binary black hole system in effective-one-body (EOB) coordinates. We implement these results based on our previous $\texttt{SEOBNRE}$ waveform model. We have also compared our model waveforms to both SXS and RIT numerical relativity waveforms. We find good consistency between our model and numerical relativity. Based on our new waveform model, we analyze the impact of the non-perpendicular spin contributions on waveform accuracy. We find that the non-perpendicular spin contributions primarily affect the phase of the gravitational waveforms. For the current gravitational wave detectors, this contribution is not significant. The future detectors may be affected by such non perpendicular spin contributions. More importantly our $\texttt{SEOBNRE}$ waveform model, as the first theoretical waveform model to describe eccentric spin-precessing binary black hole coalescence, can help people to analyze orbit eccentricity and spin precession simultaneously for gravitational wave detection data., Comment: 19 pages,12 figures

We place observational constraints on a dark energy (DE) model in which a quintessence scalar field $\phi$ is coupled to dark matter (DM) through momentum and energy exchanges.The momentum transfer is weighed by an interaction between the field derivative and DM four velocity with a coupling constant $\beta$, whereas the energy exchange is characterized by an exponential scalar-field coupling to the DM density with a coupling constant $Q$. A positive coupling $\beta$ leads to the suppression for the growth of DM density perturbations at low redshifts, whose property offers a possibility for resolving the $\sigma_8$ tension problem. A negative coupling $Q$ gives rise to a $\phi$-matter-dominated epoch, whose presence can reduce the sound horizon around the Cosmic Microwave Background (CMB) decoupling epoch. Using the data of Planck 2018, 12-th Sloan Digital Sky Survey, Phantheon supernovae samples, and 1-year dark energy survey, we find that the two couplings are constrained to be $\beta=0.332^{+1.246}_{-0.237}$ and $Q =-0.0312^{+0.0312}_{-0.0085}$ at 68\,\% confidence level (CL). Thus, there is an interesting observational signature of the momentum exchange ($\beta \neq 0$) between DE and DM, with a peak of the probability distribution of the energy transfer coupling at $Q<0$., Comment: 16 pages, 3 figures

Validating the accelerating expansion of the universe is an important issue for understanding the evolution of the universe. By constraining the cosmic acceleration parameter $X_H$, we can discriminate between the $\Lambda \mathrm{CDM}$ (cosmological constant plus cold dark matter) model and LTB (the Lema\^itre-Tolman-Bondi) model. In this paper, we explore the possibility of constraining the cosmic acceleration parameter with the inspiral gravitational waveform of neutron star binaries (NSBs) in the frequency range of 0.1Hz-10Hz, which can be detected by the second-generation space-based gravitational wave detector DECIGO. We use a convolutional neural network (CNN), a long short-term memory (LSTM) network combined with a gated recurrent unit (GRU), and Fisher information matrix to derive constraints on the cosmic acceleration parameter $X_H$. Based on the simulated gravitational wave data with a time duration of 1 month, we conclude that CNN can limit the relative error to 14.09%, while LSTM network combined with GRU can limit the relative error to 13.53%. Additionally, using Fisher information matrix for gravitational wave data with a 5-year observation can limit the relative error to 32.94%. Compared with the Fisher information matrix method, deep learning techniques will significantly improve the constraints on the cosmic acceleration parameters at different redshifts. Therefore, DECIGO is expected to provide direct measurements of the acceleration of the universe, by observing the chirp signals of coalescing binary neutron stars.

Effective one body numerical relativity waveform models for spin aligned binary black holes (SEOBNR) are based on the effective one body theoretical framework and numerical relativity simulation results. SEOBNR models have evolved through version 1 to version 4. We recently extended SEOBNRv1 model to SEOBNRE (Effective One Body Numerical Relativity waveform models for Spin aligned binary black holes along Eccentric orbit) model which is also valid for spin aligned binary black hole coalescence along eccentric orbit. In this paper we update our previous SEOBNRE model to make it consistent to SEOBNRv4 which is the most widely used SEOBNR waveform model. This upgraded SEOBNRE model improves accuracy compared to previous SEOBNRE model, especially for highly spinning black holes. For spin aligned binary black holes with mass ratio $1\leq q\lesssim10$, dimensionless spin $-0.9\lesssim\chi\lesssim0.995$ and orbital eccentricity $0\leq e_0\lesssim0.6$ at reference frequency $Mf_0=0.002$ ($M$ is the total mass of the binary black hole, $f_0\approx 40\frac{10{\rm M}_\odot}{M}$Hz), the upgraded SEOBNRE model can always fit numerical relativity waveform better than 98.2\%. For most cases the fitting factor can even be better than 99\%., Comment: 15 pages, 10 figures

The possible time variation of the fundamental constants of nature has been an active subject of research in modern physics. In this paper, we propose a new method to investigate such possible time variation of the speed of light $c$ using the updated Hubble diagram of high-redshift standard candles including Type Ia Supernovae (SNe Ia) and high-redshift quasars (based on UV-X relation). Our findings show that the SNe Ia Pantheon sample, combined with currently available sample of cosmic chronometers, would produce robust constraints on the speed of light at the level of $c/c_0=1.03\pm0.03$. For the Hubble diagram of UV+X ray quasars acting as a new type of standard candles, we obtain $c/c_0=1.19\pm0.07$. Therefore, our results confirm that there is no strong evidence for the deviation from the constant speed of light up to $z\sim 2$. Moreover, we discuss how our technique might be improved at much higher redshifts ($z\sim5$), focusing on future measurements of the acceleration parameter $X(z)$ with gravitational waves (GWs) from binary neutron star mergers. In particular, in the framework of the second-generation space-based GW detector, DECi-hertz Interferometer Gravitational-wave Observatory (DECIGO), the speed of light is expected to be constrained with the precision of $\Delta{c}/c=10^{-3}$., Comment: 11 pages,8 figures, accepted by ApJ

As the gold standard for phase retrieval, phase-shifting algorithm (PS) has been widely used in optical interferometry, fringe projection profilometry, etc. However, capturing multiple fringe patterns in PS limits the algorithm to only a narrow range of application. To this end, a deep learning (DL) model based digital PS algorithm from only a single fringe image is proposed. By training on a simulated dataset of PS fringe patterns, the learnt model, denoted PSNet, can predict fringe patterns with other PS steps when given a pattern with the first PS step. Simulation and experiment results demonstrate the PSNet's promising performance on accurate prediction of digital PS patterns, and robustness to complex scenarios such as surfaces with varying curvature and reflectance., Comment: 5 pages9 figures, a letter

Recently there are more and more interest on the gravitational wave of moving sources. This introduces a Lorentz transformation problem of gravitational wave. Although Bondi-Metzner-Sachs (BMS) theory has in principle already included the Lorentz transformation of gravitational wave, the transformation of the three dimensional gravitational wave tensor has not been explicitly calculated before. Within four dimensional spacetime, gravitational wave have property of `boost weight zero' and `spin weight 2'. This fact makes the Lorentz transformation of gravitational wave difficult to understand. In the current paper we adopt the traditional three dimensional tensor description of gravitational wave. Such a transverse-traceless tensor describes the gravitational wave freedom directly. We derive the explicit Lorentz transformation of the gravitational wave tensor. The transformation is similar to the Lorentz transformation for electric field vector and magnetic field vector which are three dimensional vectors. Based on the deduced Lorentz transformation of the gravitational wave three dimensional tensor, we can construct the gravitational waveform of moving source with any speed if only the waveform of the corresponding rest waveform is given. As an example, we apply our method to the effect of kick velocity of binary black hole. The adjusted waveform by the kick velocity is presented., Comment: 17 pages, 8 figures

Gravitational wave memory is an important prediction of general relativity. The detection of the gravitational wave memory can be used to test general relativity and to deduce the property of the gravitational wave source. Quantitative model is important for such detection and signal interpretation. Previous works on gravitational wave memory always use the energy flux of gravitational wave to calculate memory. Such relation between gravitational wave energy and memory has only been validated for post-Newtonian approximation. The result of numerical relativity about gravitational wave memory is not confident yet. Accurately calculating memory is highly demanded. Here we propose a new method to calculate the gravitational wave memory. This method is based on Bondi-Metzner-Sachs theory. Consequently our method does not need slow motion and weak field conditions for gravitational wave source. Our new method can accurately calculate memory if the non-memory waveform is known. As an example, we combine our method with matured numerical relativity result about non-memory waveform for binary black hole coalescence. We calculate the waveform for memory which can be used to aid memory detection and gravitational wave source understanding. Our calculation result confirms preliminary numerical relativity result about memory. We find out the dependence of the memory amplitude to the mass ratio and the spins of the two spin aligned black holes., Comment: 10 pages, 5 figures

Although the spatial curvature has been precisely determined via the cosmic microwave background (CMB) observation by Planck satellite, it still suffers from the well-known cosmic curvature tension. As a standard siren, gravitational waves (GWs) from binary neutron star mergers provide a direct way to measure the luminosity distance. In addition, the accelerating expansion of the universe may cause an additional phase shift in the gravitational waveform, which allows us to measure the acceleration parameter. This measurement provides an important opportunity to determine the curvature parameter $\Omega_k$ in the GW domain based on the combination of two different observables for the same objects at high redshifts. In this study, we investigate how such an idea could be implemented with future generation of space-based DECi-hertz Interferometer Gravitational-wave Observatory (DECIGO) in the framework of two model-independent methods. Our results show that DECIGO could provide a reliable and stringent constraint on the cosmic curvature at a precision of $\Delta\Omega_k$=0.12, which is comparable to existing results based on different electromagnetic data. Our constraints are more stringent than the traditional electromagnetic method from the Pantheon SNe Ia sample, which shows no evidence for the deviation from the flat universe at $z\sim 2.3$. More importantly, with our model-independent method, such a second-generation space-based GW detector would also be able to explore the possible evolution $\Omega_k$ with redshifts, through direct measurements of cosmic curvature at different redshifts ($z\sim 5$). Such a model-independent $\Omega_k$ reconstruction to the distance past can become a milestone in gravitational-wave cosmology., Comment: 10 pages, 6 figures, accepted for publication in ApJ